Shape keys not deforming correctly
Maybe your problem is the following one:
Your shapkeys are set to Relative. Let's say that you have a cube and that the shapeky #1 will be this one, i.e. vertex going up:

Now, bring back the shapekey #1 value at 0. Create your second shapekey, let's say that for this shapekey the same vertex goes up:

Now keep shapekey #2 value at 1, and move shapekey #1 value up to 1 as well, you'll see that vertex 1 will cumulate shapekey #1 and #2 effects:

I guess this it what happens here, as you've left some shapekeys value at 1, and as you've moved the same vertices in different shapekeys, their movements cumulate.
Maybe disable Relative to switch to Linear (which allows to go from a pose to another), or use bones instead of shapekeys.